PHY3062	Methods of Theoretical Physics	2013-14
	Dr M.E. Portnoi
Delivery Weeks:	T1:01-11
Level:	6 (NQF)
Credits:	15 NICATS / 7.5 ECTS
Enrolment:	67 students (approx)

Description

The mathematical techniques presented relate directly to the advanced modules at Stages 3 and 4 of Physics programmes, and also have wide applicability across the mathematical sciences. Practical skills are emphasised, rather than formal proofs.

Module Aims

This module aims to develop a deeper understanding of, and greater competence in using, some of the important mathematical methods and techniques of theoretical physics not covered in PHY2025.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. find a Laurent expansion of a function of a complex variable; identify poles and branch points;
  2. evaluate a wide variety of definite integrals using the calculus of residues;
  3. use symmetry arguments when evaluating integrals;
  4. approximate the value of a definite integral using the method of steepest descent;
  5. deduce the first term in Stirling's expansion of the factorial function;
  6. approximate the value of the ground-state energy of a bound particle by using the variational method;
  7. find approximate solutions of the Shrödinger equation using the WKB method;
  8. identify the point group of a simple symmetric object;
  9. identify the 'bond', 'site' and continuum problems of percolation theory;
  10. solve problems using the theory of conformal mapping;
• Discipline Specific Skills and Knowledge:
  11. apply analytical and numerical skills in mathematics;
  12. formulate problems in a logical manner;
• Personal and Key Transferable / Employment Skills and Knowledge:
  13. present and justify use of techniques and methods;
  14. work in groups - students are encouraged to work co-operatively together to solve assigned problems.

Syllabus Plan

1. Functions of a Complex Variable
   1. Revision of basic notations and properties of complex numbers
   2. Analytic functions
   3. Cauchy's theorem
   4. Laurent expansion
   5. Calculus of residues
2. Evaluation of Integrals
   1. Elementary methods
   2. Use of symmetry
   3. Contour integration
3. Conformal Mapping
   1. Theory
   2. Applications
4. Approximate Methods
   1. Method of steepest descent
   2. The WKB method
   3. Variational method in quantum mechanics
5. Special Chapters
   1. Elements of group theory
   2. Elements of percolation theory
   3. Non-linear Shrödinger equation (an example)

Learning and Teaching

Learning Activities and Teaching Methods

Description	Study time	KIS type
20×1-hour lectures	20 hours	SLT
2×1-hour problems/revision classes	2 hours	SLT
5×6-hour self-study packages	30 hours	GIS
4×4-hour problem sets	16 hours	GIS
Reading, private study and revision	82 hours	GIS

Assessment

Weight	Form	Size	When	ILOS assessed	Feedback
0%	Guided self-study	5×6-hour packages	Fortnightly	1-13	Discussion in class
0%	4 × Problems sets	4 hours per set	Fortnightly	1-13	Solutions discussed in problems classes.
100%	Final Examination	2 hours 30 minutes	January	1-12	Mark via MyExeter, collective feedback via ELE and solutions.

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5^th edition), Academic Press, ISBN 0-120-59826-4 (UL: 510 ARF)

Supplementary texts:

• Mathews J. and Walker R.L. (1970), Mathematical Methods of Physics (2^nd edition), Benjamin, ISBN 0-805-37002-1 (UL: 530.15 MAT)
• Stauffer D. (1985), Introduction to Percolation Theory, Taylor and Francis, ISBN 0-850-663156 (UL: 530.13 STA)

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy3062

Further Information

Prior Knowledge Requirements

Pre-requisite Modules	Mathematics with Physical Applications (PHY2025)
Co-requisite Modules	none

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment	Form of re-assessment	ILOs re-assessed	Time scale for re-assessment
Whole module	Written examination (100%)	1-12	August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods SLT - scheduled learning & teaching activities 22 hrs GIS - guided independent study 128 hrs PLS - placement/study abroad 0 hrs Total 150 hrs

Summative assessment Coursework 0% Written exams 100% Practical exams 0% Total 100%

Miscellaneous

IoP Accreditation Checklist	N/A this is an optional module
Availability	unrestricted
Distance learning	NO
Keywords	Physics; Method; Integrals; Functions; Theory; Expansion; Laurent; Variational; Calculus; Elements; Variable.
Created	01-Oct-10
Revised	N/A